I'd second exploring a path out of Mineral King. Try the Sawtooth trailhead up the old Empire Mountain trail over Glacier Pass then pass Spring Lake and the ~1000' white granite Spring Lake Wall (=similar to the Incredible Hulk), Hands and Knees Pass then drop north over a ridge to Little Five Lakes down to the Big Arroyo. Scramble up Black Kaweah's SW chute, then pick and scenic loop out. I'd suggest popping over Kaweah gap to Hamilton Lakes then looping back to Mineral King. Almost anywhere along the way will have spectacular camping and peaks to scramble.